One-Loop MHV Amplitudes in Supersymmetric Gauge Theories

TL;DR

The paper tests the CSW/MHV-diagram formalism for one-loop amplitudes in massless supersymmetric gauge theories by computing the N=1 chiral multiplet contribution to the one-loop MHV gluon amplitude and matching a known unitarity-based result.Using CSW rules, the authors express the loop integrals in terms of off-shell MHV vertices and demonstrate that, after Schouten manipulations, the integrand decomposes into tensor box, two-mass triangle, and IR components with correct coefficients.They perform explicit cut calculations in all channels and show that dispersion over the light-cone parameters reproduces the finite box and triangle functions, with bubble terms canceling across diagrams.The result confirms the validity of the MHV-diagram approach for this amplitude in any massless SUSY theory at one loop and suggests cut-constructibility as a central mechanism behind the method's success.

Abstract

Using CSW rules for constructing scalar Feynman diagrams from MHV vertices, we compute the contribution of $\mathcal {N}=1$ chiral multiplet to one-loop MHV gluon amplitude. The result agrees with the one obtained previously using unitarity-based methods, thereby demonstrating the validity of the MHV-diagram technique, in the case of one-loop MHV amplitudes, for all massless supersymmetric theories.

Figures (5)

• Figure 1: Diagrams contributing to box functions.
• Figure 2: Diagrams contributing to triangle functions.
• Figure 3: Two of the degenerate triangle diagrams, the other two are obtained by exchanging $p$ and $q$ .
• Figure 4: Typical one-loop MHV diagram, one has to sum over all choices of $m_1,m_2$. The negative helicity gluon $p$ is on the left, and $q$ is on the right.
• Figure 5: One MHV diagram produces 4 cut boxes and triangles, one for each dashed line. Where exactly the cut lies depends on $r,s$. Therefore, a given box (triangle) with $r,s$ fixed requires 4 (2) MHV diagrams to produce all of its cuts.